Question: Expand $(x^{22}-3x^{5} + x^{-2} - 7)\cdot(5x^4)$.
Using the distributive property, we can expand this to get \begin{align*}
(x^{22}&-3x^{5} + x^{-2} - 7)\cdot(5x^4)\\
&=(x^{22})(5x^4)+(-3x^5)(5x^4)+(x^{-2})(5x^4)-7(5x^4)\\
&=5x^{26}-15x^9+5x^2-35x^4\\
&=\boxed{5x^{26}-15x^9-35x^4+5x^2}.
\end{align*}